Given:
- Base of the isosceles triangle = 12 cm
- Perimeter of the triangle = 35 cm

To Find:
- Area of the triangle

Solution:
Step 1: Determine the length of the equal sides (legs) of the triangle.
Since the triangle is isosceles, it has two equal sides. Let the length of each equal side be 'x'.

Step 2: Calculate the perimeter of the triangle.
Perimeter = Sum of all three sides
35 cm = 12 cm + x + x

Simplifying the equation,
35 cm = 12 cm + 2x
2x = 35 cm - 12 cm
2x = 23 cm
x = 23 cm / 2
x = 11.5 cm

Therefore, each equal side of the isosceles triangle is 11.5 cm long.

Step 3: Calculate the height of the triangle.
The height of an isosceles triangle is a perpendicular line segment drawn from the vertex (topmost point) to the base, bisecting it.
We can use the Pythagorean theorem to find the height.

Let the height of the triangle be 'h'.
Using the Pythagorean theorem,
h^2 = x^2 - (1/2 * base)^2
h^2 = 11.5 cm^2 - (1/2 * 12 cm)^2
h^2 = 11.5 cm^2 - 6 cm^2
h^2 = 132.25 cm^2 - 36 cm^2
h^2 = 96.25 cm^2
h = √(96.25 cm^2)
h ≈ 9.812 cm

Therefore, the height of the triangle is approximately 9.812 cm.

Step 4: Calculate the area of the triangle.
Area of a triangle = (1/2) * base * height
Area = (1/2) * 12 cm * 9.812 cm
Area ≈ 58.872 cm^2

Therefore, the area of the isosceles triangle is approximately 58.872 cm^2.